% Appendix C - Optimal Fusion Weights

\chapter{Optimal Fusion Weights}
\label{app:optimal-weights}
\lhead{Appendix C. \emph{Optimal Fusion Weights}}



In this appendix we list the optimal run weights for the ten weighted fusion experiments described in Chapter \ref{chapter6}. We list the optimal weights for each of our four data sets separately in Tables \ref{table:weights-bib-boo} through \ref{table:weights-cul}. Table \ref{table:fusion-run-ids} lists the IDs we use to refer to the individual runs in those four tables.

\begin{table}[htp]
  \caption[Run IDs used in Tables \ref{table:weights-bib-boo}--\ref{table:weights-cul}]{Run IDs used in Tables \ref{table:weights-bib-boo}--\ref{table:weights-cul}.}
  \begin{center}
  \begin{small}
  \begin{tabular}{c|l}
  \hline
  {\bf Run ID} & {\bf Run description}  \\
  \hline
  \hline
  {\bf R1}     & Best user-based run based on usage similarity (from Section \ref{4:sec:cf}) \\
  {\bf R2}     & Best item-based run based on usage similarity (from Section \ref{4:sec:cf}) \\
  {\bf R3}     & Best user-based run based on tag overlap similarity (from Subsection \ref{4:subsec:tagging-overlap}) \\
  {\bf R4}     & Best item-based run based on tag overlap similarity (from Subsection \ref{4:subsec:tagging-overlap}) \\
  {\bf R5}     & Best profile-centric run based on metadata (from Subsection \ref{5:subsec:content-based-filtering}) \\
  {\bf R6}     & Best post-centric run based on metadata (from Subsection \ref{5:subsec:content-based-filtering}) \\
  {\bf R7}     & Best user-based run based on metadata (from Subsection \ref{5:subsec:hybrid-filtering}) \\
  {\bf R8}     & Best item-based run based on metadata (from Subsection \ref{5:subsec:hybrid-filtering}) \\
  \hline
  \end{tabular}
  \end{small}
  \end{center}
  \label{table:fusion-run-ids}
\end{table}



\begin{table}[htp]
  \caption[Optimal fusion weights for Bibsonomy bookmarks data set]{Optimal fusion weights for the different fusion experiments on the Bibsonomy bookmarks data set.}
  \begin{center}
  \begin{small}
  \begin{tabular}{l|l||c|c|c|c|c|c|c|c}
  \hline
   {\bf Run ID}   & {\bf Method} 
                  & {\bf R1} & {\bf R2} & {\bf R3} & {\bf R4} 
                  & {\bf R5} & {\bf R6} & {\bf R7} & {\bf R8}  \\
  \hline
  \hline
  \multirow{3}{*}{{\bf Fusion A}} &  Weighted \combsum  
                  & 0.3  & 1.0   & -   & -   & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & 0.3  & 1.0   & -   & -   & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & 0.2  & 1.0   & -   & -   & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion B}} &  Weighted \combsum  
                  & -     & -     & 0.4  & 1.0 & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & 0.4  & 0.8 & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & -     & -     & 0.4  & 0.9 & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion C}} &  Weighted \combsum  
                  & 0.5   & -     & -   & 0.7 & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & 0.2   & -     & -   & 0.8 & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & 0.3   & -     & -   & 0.8 & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion D}} &  Weighted \combsum  
                  & -     & -     & -   & -   & 1.0  & 0.1 & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & 1.0  & 0.1 & -   & -  \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & 0.9  & 1.0 & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion E}} &  Weighted \combsum  
                  & -     & -     & -   & -   & -   & -   & 0.5  & 0.7 \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & -   & -   & 0.1  & 0.9 \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & -   & -   & 0.7  & 1.0 \\
  \hline
  \multirow{3}{*}{{\bf Fusion F}} &  Weighted \combsum  
                  & -     & -     & -   & -   & 1.0 & -   & -   & 0.4 \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & 0.5 & -   & -   & 0.2 \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & 0.1 & -   & -   & 0.9 \\
  \hline
  \multirow{3}{*}{{\bf Fusion G}} &  Weighted \combsum  
                  & -     & -     & -   & 0.5 & 0.7 & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & 0.2 & 0.9 & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & 1.0 & 0.2 & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion H}} &  Weighted \combsum  
                  & 0.3  & 0.9  &  0.4 &  0.8  & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & 0.2  & 1.0  &  0.3 &  1.0  & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & 0.1  & 1.0  &  0.2 &  0.4 & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion I}} &  Weighted \combsum  
                  & -     & -     & -   & -   & 0.3  & 0.1  &  0.5 &  0.7 \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & 0.3  & 0.4  &  0.2 &  0.8 \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & 0.3  & 0.4  &  0.2 &  1.0  \\
  \hline
  \multirow{3}{*}{{\bf Fusion J}} &  Weighted \combsum  
                  & 0.3  & 0.8  &  0.3 &  0.6 &  0.9 &  0.8 &  0.0 &  0.8 \\
  ~                               &  Weighted \combmnz 
                  & 0.5  & 0.7  &  0.4 &  1.0 &  0.9 &  0.4 &  0.0 &  0.7 \\
  ~                               &  Weighted \combanz 
                  & 0.2  & 0.6  &  0.2 &  0.8 &  0.0 &  0.9 &  0.6 &  1.0 \\
  \hline
  \end{tabular}
  \end{small}
  \end{center}
  \label{table:weights-bib-boo}
\end{table}

~\\

\newpage

\begin{table}[htp]
  \caption[Optimal fusion weights for Delicious bookmarks data set]{Optimal fusion weights for the different fusion experiments on the Delicious bookmarks data set.}
  \begin{center}
  \begin{small}
  \begin{tabular}{l|l||c|c|c|c|c|c|c|c}
  \hline
   {\bf Run ID}   & {\bf Method} 
                  & {\bf R1} & {\bf R2} & {\bf R3} & {\bf R4} 
                  & {\bf R5} & {\bf R6} & {\bf R7} & {\bf R8}  \\
  \hline
  \hline
  \multirow{3}{*}{{\bf Fusion A}} &  Weighted \combsum  
                  & 0.6  & 1.0   & -   & -   & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & 0.9  & 0.9   & -   & -   & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & 1.0  & 0.9   & -   & -   & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion B}} &  Weighted \combsum  
                  & -     & -     & 0.0  & 1.0 & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & 0.0  & 1.0 & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & -     & -     & 0.0  & 0.9 & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion C}} &  Weighted \combsum  
                  & 0.1   & -     & -   & 1.0 & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & 0.0   & -     & -   & 0.9 & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & 0.1   & -     & -   & 1.0 & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion D}} &  Weighted \combsum  
                  & -     & -     & -   & -   & 0.0  & 0.9 & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & 0.0  & 0.7 & -   & -  \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & 0.0  & 0.9 & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion E}} &  Weighted \combsum  
                  & -     & -     & -   & -   & -   & -   & 1.0  & 0.8 \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & -   & -   & 1.0  & 0.0 \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & -   & -   & 0.4  & 1.0 \\
  \hline
  \multirow{3}{*}{{\bf Fusion F}} &  Weighted \combsum  
                  & -     & -     & -   & -   & - & 0.9  & 0.6 & - \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & - & 0.7  & 0.2 & - \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & - & 1.0  & 0.5 & - \\
  \hline
  \multirow{3}{*}{{\bf Fusion G}} &  Weighted \combsum  
                  & -     & -     & -   & 0.9 & - & -   & 0.0   & -  \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & 0.9 & - & -   & 0.0   & -  \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & 1.0 & - & -   & 0.1   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion H}} &  Weighted \combsum  
                  & 0.2  & 0.3  &  0.1 &  0.6 & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & 0.0  & 0.3  &  0.0 &  0.9 & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & 0.4  & 0.3  &  0.1 &  1.0 & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion I}} &  Weighted \combsum  
                  & -     & -     & -   & -   & 0.0  & 0.6  &  0.4 &  0.9 \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & 0.0  & 0.7  &  0.5 &  0.9 \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & 0.2  & 0.9  &  0.2 &  0.9  \\
  \hline
  \multirow{3}{*}{{\bf Fusion J}} &  Weighted \combsum  
                  & 0.2  & 0.5  &  0.1 &  0.7 &  0.1 &  0.5 &  0.0 &  0.2 \\
  ~                               &  Weighted \combmnz 
                  & 0.7  & 0.9  &  0.2 &  1.0 &  0.2 &  0.9 &  0.1 &  0.9 \\
  ~                               &  Weighted \combanz 
                  & 0.8  & 0.8  &  0.2 &  0.5 &  0.0 &  1.0 &  0.4 &  0.9 \\
  \hline
  \end{tabular}
  \end{small}
  \end{center}
  \label{table:weights-del}
\end{table}

~\\

\newpage

\begin{table}[htp]
  \caption[Optimal fusion weights for Bibsonomy articles data set]{Optimal fusion weights for the different fusion experiments on the Bibsonomy articles data set.}
  \begin{center}
  \begin{small}
  \begin{tabular}{l|l||c|c|c|c|c|c|c|c}
  \hline
   {\bf Run ID}   & {\bf Method} 
                  & {\bf R1} & {\bf R2} & {\bf R3} & {\bf R4} 
                  & {\bf R5} & {\bf R6} & {\bf R7} & {\bf R8}  \\
  \hline
  \hline
  \multirow{3}{*}{{\bf Fusion A}} &  Weighted \combsum  
                  & 0.9  & 0.2   & -   & -   & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & 0.9  & 0.2   & -   & -   & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & 0.8  & 0.5   & -   & -   & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion B}} &  Weighted \combsum  
                  & -     & -     & 0.1  & 0.7 & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & 0.0  & 1.0 & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & -     & -     & 0.1  & 0.9 & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion C}} &  Weighted \combsum  
                  & 1.0   & -     & -   & 0.7 & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & 1.0   & -     & -   & 0.4 & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & 0.3   & -     & -   & 0.8 & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion D}} &  Weighted \combsum  
                  & -     & -     & -   & -   & 0.9  & 0.3 & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & 0.9  & 0.3 & -   & -  \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & 0.1  & 1.0 & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion E}} &  Weighted \combsum  
                  & -     & -     & -   & -   & -   & -   & 0.1  & 0.9 \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & -   & -   & 0.0  & 0.9 \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & -   & -   & 0.1  & 0.7 \\
  \hline
  \multirow{3}{*}{{\bf Fusion F}} &  Weighted \combsum  
                  & -     & -     & -   & -   & 0.8 & -   & -   & 0.5 \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & 0.8 & -   & -   & 0.5 \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & 0.1 & -   & -   & 1.0 \\
  \hline
  \multirow{3}{*}{{\bf Fusion G}} &  Weighted \combsum  
                  & -     & -     & -   & 0.7 & -   & -   & -   & 1.0  \\
  ~                               &  Weighted \combmnz  
                  & -     & -     & -   & 0.0 & -   & -   & -   & 0.9  \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & 1.0 & -   & -   & -   & 0.7  \\
  \hline
  \multirow{3}{*}{{\bf Fusion H}} &  Weighted \combsum  
                  & 1.0  & 0.2  &  0.1 &  0.7 & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & 0.8  & 0.6  &  0.0 &  0.2 & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & 0.4  & 0.4  &  0.1 &  0.7 & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion I}} &  Weighted \combsum  
                  & -     & -     & -   & -   & 0.8  & 0.2  &  0.1 &  0.3 \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & 0.7  & 0.6  &  0.1 &  1.0 \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & 0.1  & 0.5  &  0.1 &  0.8 \\
  \hline
  \multirow{3}{*}{{\bf Fusion J}} &  Weighted \combsum  
                  & 1.0  & 0.1  &  0.4 &  0.4 &  1.0 &  0.4 &  0.0 &  0.9 \\
  ~                               &  Weighted \combmnz 
                  & 0.9  & 0.3  &  1.0 &  0.9 &  0.5 &  0.0 &  0.2 &  1.0 \\
  ~                               &  Weighted \combanz 
                  & 0.6  & 0.4  &  0.6 &  0.8 &  0.1 &  0.9 &  0.2 &  1.0 \\
  \hline
  \end{tabular}
  \end{small}
  \end{center}
  \label{table:weights-bib-art}
\end{table}

~\\

\newpage

\begin{table}[htp]
  \caption[Optimal fusion weights for CiteULike bookmarks data set]{Optimal fusion weights for the different fusion experiments on the CiteULike bookmarks data set.}
  \begin{center}
  \begin{small}
  \begin{tabular}{l|l||c|c|c|c|c|c|c|c}
  \hline
   {\bf Run ID}   & {\bf Method} 
                  & {\bf R1} & {\bf R2} & {\bf R3} & {\bf R4} 
                  & {\bf R5} & {\bf R6} & {\bf R7} & {\bf R8}  \\
  \hline
  \hline
  \multirow{3}{*}{{\bf Fusion A}} &  Weighted \combsum  
                  & 0.2  & 0.8   & -   & -   & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & 0.1  & 0.6   & -   & -   & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & 0.1  & 1.0   & -   & -   & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion B}} &  Weighted \combsum  
                  & -     & -   & 0.2  & 0.8 & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & -     & -   & 0.1  & 0.7 & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & -     & -   & 0.1  & 0.6 & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion C}} &  Weighted \combsum  
                  & -     & 0.7   & -   & 0.4 & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & -     & 1.0   & -   & 0.4 & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & -     & 0.7   & -   & 0.9 & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion D}} &  Weighted \combsum  
                  & -     & -     & -   & -   & 1.0  & 0.2 & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & 1.0  & 0.2 & -   & -  \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & 0.0  & 1.0 & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion E}} &  Weighted \combsum  
                  & -     & -     & -   & -   & -   & -   & 0.1  & 0.9 \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & -   & -   & 0.1  & 1.0 \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & -   & -   & 0.1  & 0.8 \\
  \hline
  \multirow{3}{*}{{\bf Fusion F}} &  Weighted \combsum  
                  & -     & -     & -   & -   & 0.7 & -   & -   & 0.5 \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & 1.0 & -   & -   & 0.4 \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & 0.1 & -   & -   & 0.9 \\
  \hline
  \multirow{3}{*}{{\bf Fusion G}} &  Weighted \combsum  
                  & -     & 1.0 & -     & -   & 0.7 & -   & -   & -    \\
  ~                               &  Weighted \combmnz  
                  & -     & 1.0 & -     & -   & 0.7 & -   & -   & -    \\
  ~                               &  Weighted \combanz 
                  & -     & 1.0 & -     & -   & 0.1 & -   & -   & -    \\
  \hline
  \multirow{3}{*}{{\bf Fusion H}} &  Weighted \combsum  
                  & 0.3  & 0.8  &  0.0 &  1.0 & -   & -   & -   & -  \\
  ~                               &  Weighted \combmnz 
                  & 0.1  & 0.8  &  0.0 &  0.5 & -   & -   & -   & -  \\
  ~                               &  Weighted \combanz 
                  & 0.1  & 0.9  &  0.0 &  0.5 & -   & -   & -   & -  \\
  \hline
  \multirow{3}{*}{{\bf Fusion I}} &  Weighted \combsum  
                  & -     & -     & -   & -   & 1.0  & 0.1  &  0.1 &  0.3 \\
  ~                               &  Weighted \combmnz 
                  & -     & -     & -   & -   & 0.8  & 0.2  &  0.1 &  0.1 \\
  ~                               &  Weighted \combanz 
                  & -     & -     & -   & -   & 0.0  & 0.9  &  0.1 &  0.9 \\
  \hline
  \multirow{3}{*}{{\bf Fusion J}} &  Weighted \combsum  
                  & 0.4  & 1.0  &  0.3 &  0.7 &  1.0 &  0.5 &  0.0 &  0.7 \\
  ~                               &  Weighted \combmnz 
                  & 0.4  & 1.0  &  0.1 &  0.2 &  0.2 &  0.8 &  0.0 &  0.1 \\
  ~                               &  Weighted \combanz 
                  & 0.3  & 1.0  &  0.6 &  1.0 &  0.1 &  1.0 &  0.4 &  1.0 \\
  \hline
  \end{tabular}
  \end{small}
  \end{center}
  \label{table:weights-cul}
\end{table}

~\\

\newpage

~\\

\newpage

\makeemptypage